Computer

Some basic concepts

Binary number

Why binary? Look at a decimal number: 3511 Look at a binary number: 1011 counting

decimal 0 1 2 3 4 5 6 7 8 9

binary 0 1 10 11 100

Binary number

Maximum possible8 bits: 40 bits: N bits:

What is the number after 10111?

Hexadecimal

Decimal: base 10 Binary: base 2 Hexadecimal: base 16 But works the same way Translate F1C: Where do you see it?

decimal binary hexadecimal

0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 0101 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A 11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F

Size

1 byte = 8 bits 1KB = 2^10 bytes 1MB = 2^20 bytes 1GB = 2^30 bytes 1TB = 2^40 bytes

ASCII

ASCII (American Standard Code for Information Interchange)

How to represent a keyboard character as a number?

Assigns a unique number (0-127) to each keyboard character.

Examples: a - 97 A to Z: 65-90 a to z: 97-122 0 to 9: 48-57

Unicode

127 is not enough Other languages Same principle More characters

Digitizing the world

Example: Digitizing Sound

An object creates sound by vibrating in a medium such as air

Vibrations push the air

Pressure waves emanate from the object and vibrate our eardrums

The force, or intensity of the push determines the volume

The frequency (number of waves per second) is the pitch

Analog to Digital

To convert continuous information, convert it to bits

From zero line on graph, record with binary number the amount by which the wave is above or below it (positive or negative sound pressure)

At what points do we measure? We can't record every position of the wave

Sampling

Take measurements at regular intervals

Number of samples in a second is the sampling rate The faster the rate, the

more accurate the recording

How Fast to Sample?

Sampling rate should be related to the wave's frequency

Too slow rate could allow waves to fit between the samples; we'd miss segments of sound

Guideline is Nyquist Rule: Sampling rate must be at least twice as fast as the fastest frequency

Human perception can hear sound up to 20,000 Hz, so 40,000 Hz sampling rate is enough.

Standard for digital audio is 44,100 Hz

How Many Bits per Sample?

How accurate must the samples be?

Bits must represent both positive and negative values

The more bits, the more accurate the measurement

The digital representation of audio CDs uses 16 bits (records 65,536 levels, half above and half below the zero line)

How large is one-minute music?

One-minute digital audio?60 seconds44,100 samples16 bits eachTimes 2 for stereo60*44,100*2(Bytes)*2=10.5 MB!

An hour is 635MB!

ADC, DAC

Digitizing Process: Sound is picked up by a microphone

(called a transducer)

The signal is fed into an analog-to-digital converter (ADC), which samples it at regular intervals and outputs binary numbers to memory

To play the sound, the process is reversed Numbers are read from memory into digital-to-analog converter (DAC),

which creates an electrical wave by filling in between the digital values Electrical signal is output to speaker, which converts it to a sound

wave

Advantages of Digital Sound (MP3) Compression

One computation is to compress the digital audio (reduce number of bits needed)

Remove waves that are outside range of human hearing Teen-only ringtone MP3 usually gets a compression rate of 10:1

Lower bandwidth requirements, popular for Internet transmission

Reproducing the Sound Recording Bit file can be copied without losing any information Original and copy are exactly the same Vinyl recording is analog, it wears out. Easy “transportation”

We can compute the representation Enhance, manipulate Synthetic voice